# Can Someone Help Me With Formulas And Key Points , Urgent And Easy Please ?

Formulas And Key Points For The Following :

(1) Simplifying And Expressing Single Fraction

(3) Complex fraction

(4) Simultaneous Equations By Substitution Method

(5) Factorizing Using Grouping

Relevance

The easiest way to explain is to give examples. Unfortunately I do not have too much time available so I shall only do 4) Substitution method simultaneous equations now.

2x + 4y = 22

6x + 3y = 39

(NB If you have an example where x or y do not have coefficients in either of the equations then use that, as it will save work)

Step 1

Isolate one of the variables on one side of the equals sign in either one of the equations.

Here I shall take the top equation and isolate "x"

2x+ 4y = 22

Subtract 4y from both sides

2x = 22 - 4y

divide both sides by 2

x = 11 - 2y

Therefore now we have an identity for "x"

STEP 2

Use this by SUBSTITUTING (11 -2y) for "x" in the bottom equation

This now becomes

6(11 -2y) + 3y = 39

Expand the bracket

66 - 12y + 3y = 39

simplify

66 - 9y = 39

Add 9y and subtract 39 from each side

27 = 9y

Divide both sides by 9

27/9 = y

3 = y

STEP 3

Now SUBSTITUTE "3" for "y" in the equation x = 11 - 2y

x = 11 - 2*3

x = 11 - 6

x = 5

Therefore the solution is x = 5, y = 3 which can also be written as

Solution (5,3)

STEP 4

Now check the answer to ensure that we have not made any errors

2x + 4y = 22

2*5 + 4*3 = 22

10 + 12 = 22 = Correct

and

6x + 3y = 39

6*5 + 3*3 = 39

30 + 9 =39 = Correct